A generalized model for the transverse fluid permeability in unidirectional fibrous media

In liquid molding processes such as resin transfer molding (RTM), fluid is injected into a mold filled with fiber reinforcement. The microstructure of the reinforcement strongly influences the resistance it offers to fluid flow. This resistance is characterized by the permeability that determines the ratio between the superficial velocity and the pressure drop in the porous medium. Currently values of the permeability have to be determined experimentally. Therefore, each type of reinforcement has to be characterized before a computer simulation can be used to predict the overall mold filling pattern. A model for predicting the permeability as a function of structure would help reduce the number of experiments needed to determine the input parameters for mold filling simulations. Also, by understanding the physics of the flow through such materials, one may tailor the microstructure such that it has both the desired reinforcing capability and the necessary permeability to fill efficiently. In response to this need, we have developed a predictive semi analytical solution for flow across arrays of aligned cylinders with elliptical cross sections modeling the fiber mats. The shape of the tow, its porosity, and the packing configuration are found to influence the transverse permeability of such an array significantly. Predicted results of the permeability from this model compare very well with numerical results obtained from finite element calculations over a range of volume fractions, cross-sectional shapes, and tow permeabilities.